2001/11/08 by Tyler J. Evans, Evans, Tyler J.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.math/0111090
Dissertation
arxiv created 2001/11/08 · openalex publication_date 2001/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this dissertation, we investigate the cohomology theory of restricted Lie algebras. The representation theory of restricted Lie algebras is reviewed including a description of the restricted universal enveloping algebra. In the case of an abelian restricted Lie algebra, we construct an augmented complex of free modules over the enveloping algebra that is exact in dimensions less than p and hence define the cohomology theory of these algebras in dimension less than p. In the non-abelian case, we explicitly construct cochain spaces for any coefficient module in dimensions less than 3, and give explicit formulas for the coboundary operators in these dimensions. The corresponding notions of the usual algebraic interpretations of ordinary low dimensional cohomology are defined and we show that our restricted cohomology spaces encode this information as well.